[From Bill Powers (930315.2100)]
Martin Taylor (930315.1800) --
I understand that the gain cannot usefully be infinite if there
is any noise in the perception, which means that the perception
can correspond exactly and immediately to the real-world
construct we call the CEV. I understand that such conditions
do not exist in the real world.
I almost let this pass without comment -- I'm spending a whole
lot of time at the keyboard and beginning to feel swamped.
Nobody - neither Rick nor I -- has ever said that the state of
the CEV is not represented in the perceptual signal. Nor have we
said that a change in the CEV is not (more or less) faithfully
rendered as a change in the perceptual signal, or that the
perceptual signal contains no information about the CEV or
changes in the CEV. What we have said is that the perceptual
signal does not contain (usable) information about the
_disturbance_.
Just today, Allan Randall defined the disturbance as a change in
the CEV, and I wrote a correction of that idea. Now I infer,
perhaps incorrectly, that you, too, are defining the disturbance
as a change in the CEV. Once before, I seem to remember, you
expressed puzzlement as to why I insisted on introducing a
separate disturbing variable -- you seemed to consider it
superfluous. Is the same thing recurring?
Consider the rubber-band experiment. The disturbing variable is
the position of the experimenter's end of the rubber-bands. The
controlled variable -- the CEV -- is the position of the knot
relative to the dot. The experimenter applies a disturbance by
changing the state of the disturbing variable, his end of the
rubber bands, not by grasping the knot, the CEV, and arbitrarily
moving it.
This is critical. If the experimenter arbitrarily moves the knot,
the subject will lose control completely and nothing will be
learned about the control system. The subject will probably stop
trying to control and complain, asking how it is possible to
control the knot while the experimenter has hold of it.
When the experimenter varies the state of the disturbing variable
by moving his end of the rubber bands in a reasonably smooth way,
there is no way to predict how the CEV will vary; that is
determined as much by the actions of the person on the other end
of the experiment as by the experimenter. For any static state of
the disturbing variable, the CEV might end up in any state,
including no deflection at all.
The disturbing variable is an independent variable with respect
to the control system. It can be set independently. The CEV is
not an independent variable, at least while the control system is
functioning normally.
Could this whole argument have arisen over a difference in
understanding of what is meant by "disturbance?"
Best,
Bill P.